Barack Obama has praised Ted Kennedy as one of the "most accomplished Americans" to serve his country as he led the tributes for the last surviving brother from his generation of America's leading political dynasty.

In a brief statement from Martha's Vineyard, where he is on holiday, the US president described Kennedy as someone who had touched many lives with his ideas and ideals, and whose work in Congress helped give millions new opportunities. "Including myself," said America's first black president.

Earlier, Obama said he and his wife, Michelle, were "heartbroken" to hear of Kennedy's death. As tributes poured in from across the world, Obama spoke of his gratitude to America's elder statesman and of Kennedy's indelible mark on US politics.

"I valued his wise counsel in the Senate, where, regardless of the swirl of events, he always had time for a new colleague," Obama said. "I cherished his confidence and momentous support in my race for the presidency."

Obama stressed Kennedy's political contribution, saying: "An important chapter in our history has come to an end. Our country has lost a great leader, who picked up the torch of his fallen brothers and became the greatest United States senator of our time."

"Edward M Kennedy, the husband, father, grandfather, brother and uncle we loved so deeply, died late Tuesday night at home in Hyannis Port (Massachusetts)," the family said in a statement. "We've lost the irreplaceable centre of our family and joyous light in our lives, but the inspiration of his faith, optimism and perseverance will live on in our hearts forever."

Kennedy, who died at the age of 77, was diagnosed with a brain tumour in May 2008. Like his two assassinated brothers – President John Kennedy and the presidential candidate Robert Kennedy – he had been expected to scale great political heights. The fourth brother, Joe, was a pilot killed in the second world war.

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Kennedy's career was significantly blighted by the Chappaquiddick incident of 1969 in which the car he was driving ran off a bridge and plunged into the water, killing his passenger Mary Jo Kopechne. While he never reached the pinnacle of power, Kennedy eventually shed his playboy image to become a serious political presence in the Senate. His death marks the twilight of a political dynasty and deals a blow to Democrats as they seek an overhaul of the healthcare system, one of Kennedy's personal goals.

When Kennedy first took the Senate seat previously held by John in 1962 he was seen as something of a political lightweight who owed his ascent to his famous name. Yet during his near half-century in the chamber Kennedy turned into one of Washington's most effective operators, crafting legislation by working with colleagues and presidents of both parties and finding unlikely allies.

At the same time he clung to liberal causes and was considered a political dinosaur by centrist "New Democrats" and rightwing Republicans. He helped enact measures to protect civil and labour rights, expand healthcare, upgrade schools, increase student aid and contain the spread of nuclear weapons.

"There's a lot to do," said Kennedy in 2006. "I think most of all it's the injustice that I continue to see and the opportunity to have some impact on it."

After Robert Kennedy's death in 1968, Ted was expected to emulate his brothers' presidential ambitions. But then came Chappaquiddick. Kennedy's image suffered irreparable damage when it emerged that he had failed to immediately report the accident to authorities. He pleaded guilty to leaving the scene and received a suspended sentence.

Kennedy eventually ran for his party's presidential nomination in 1980 but lost to the incumbent president, Jimmy Carter, his reputation taking another knock after failing to answer a TV interviewer's question about why he wanted to become America's leader.

His presidential ambitions thwarted, Kennedy devoted himself to the Senate, where he was the moving force behind several important pieces of legislation on social issues, including a rise in the minimum wage.

Kennedy's endorsement in the 2008 Democratic primary – much to the disappointment of Hillary and Bill Clinton – was seen as a huge boost to Obama's campaign. Obama said that as president he benefited from Kennedy's "encouragement and wisdom" even as the senator battled brain cancer.

As world leaders paid their tributes, Gordon Brown, the British prime minister, said Kennedy would be "mourned not just in America but in every continent".

Tributes came from across the political spectrum – testimony to his ability to form close bonds with political opponents. The former first lady Nancy Reagan said: "Given our political differences, people are sometimes surprised by how close Ronnie and I have been to the Kennedy family. In recent years Ted and I found our common ground in stem cell research, and I considered him an ally and a dear friend. I will miss him."